Aerospace and Electronic Systems Magazine February 2018 - 47

Ahmadi, Kosari, and Malaek
If Q > 1, then an image with good quality could be provided so
Q could be considered constant and equal to 1.1.
As depicted in Figure 10, the allowable design area will be
between the shortest wavelength with the smallest pixel size (Blue
- x = 2 μm) and the longest wavelength with the largest pixel size
(NIR - x = 14 μm).
According to the results of sizing to spatial resolution requirements, it is allowed to use only detector elements with size
x = 2 μm in the sensor. Since the shortest wavelength (Blue
- λ = 0.475 μm) also covers the requirements of other wavelengths, then the next calculations could be performed only for
this wavelength and the results could be generalized to the other
wavelengths.
3. Sizing to Image Quality Requirements.
By eliminating x (detector element size) from (6) and (9), (10)
could be reached.
f
1 λ f
=
H Q GSD D

Figure 10.

Sizing to spectral resolution.

(10)

In Figure 12, the graphs of F# vs. x have been drawn for different values of Q. The boundary values of F# (DD, f/D) has been
specified in this graph. Based on the lens manufacturing technological constraints the allowable F# must be in
the below interval:
1.2 ≤ F# ≤ 2.8
As could be seen in Figure 12, there are four
points in the allowable area where the boundary values of F# define its borders. For better
display, the allowable area in Figure 11 has been
shown from a closer view in Figure 12.
The PDs which based on their F# value and
their detector element size are placed in the allowable area, have been listed in Table 10 and
they are shown in the design plane in Figure 13.
The following points could be inferred using
Figure 13:
C Among

the PDs, the point which has the higher value of f/D, also has the higher value of Q.

Figure 12.

Figure 11.

F# vs. x for different values of Q and the allowable
area from the close view.

F# vs. x for different values of Q.

FEBRUARY 2018

IEEE A&E SYSTEMS MAGAZINE

47



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